On the asymptotic behaviour of solutions of the Dirac system and applications to the Sturm–Liouville problem with a singular potential
Alexander Gomilko
Nicolaus Copernicus University, Toruń, PolandŁukasz Rzepnicki
Nicolaus Copernicus University, Toruń, Poland
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Abstract
The main focus of this paper is the following matrix Cauchy problem for the Dirac system on the interval [0,1]:
where is a spectral parameter, and , . We propose a new approach for the study of asymptotic behaviour of its solutions as and . As an application, we obtain new, sharp asymptotic formulas for eigenfunctions of Sturm–Liouville operators with singular potentials.
Cite this article
Alexander Gomilko, Łukasz Rzepnicki, On the asymptotic behaviour of solutions of the Dirac system and applications to the Sturm–Liouville problem with a singular potential. J. Spectr. Theory 10 (2020), no. 3, pp. 747–786
DOI 10.4171/JST/311